A184889 a(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+2)*(10k+3).

1, 30, 5850, 1644500, 542685000, 196017822000, 75031266310000, 29905319000700000, 12279871614662437500, 5159062111690898125000, 2207046771381366217875000, 958150139674902210123750000

Offset: 0

Author

Paul D. Hanna, Jan 25 2011

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 30*x + 5850*x^2 + 1644500*x^3 +...
A(x)^2 = 1 + 60*x + 12600*x^2 + 3640000*x^3 +...+ A184890(n)*x^n +...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A184890, A184891.

Programs

Mathematica

FullSimplify[Table[500^n * Gamma[n+1/5] * Gamma[n+3/10] / (Gamma[n+1]^2 * Gamma[1/5] * Gamma[3/10]), {n, 0, 15}]] (* Vaclav Kotesovec, Jul 03 2014 *)
Join[{1},With[{nn=15},Table[5^n/(n!)^2,{n,nn}] Rest[FoldList[Times,1, Table[ (10k+2)(10k+3),{k,0,nn-1}]]]]] (* Harvey P. Dale, Sep 20 2014 *)

PARI

{a(n)=(5^n/n!^2)*prod(k=0,n-1,(10*k+2)*(10*k+3))}

Formula

Self-convolution yields Sum_{k=0..n} a(n-k)*a(k) = A184890(n) where A184890(n) = C(2n,n) * (5^n/n!^2)*Product_{k=0..n-1} (5k+2)*(5k+3).